Termination w.r.t. Q of the following Term Rewriting System could be proven:

Q restricted rewrite system:
The TRS R consists of the following rules:

a(a(a(x1))) → b(b(x1))
b(b(b(x1))) → c(x1)
c(x1) → d(d(x1))
d(x1) → a(a(x1))

Q is empty.


QTRS
  ↳ DirectTerminationProof

Q restricted rewrite system:
The TRS R consists of the following rules:

a(a(a(x1))) → b(b(x1))
b(b(b(x1))) → c(x1)
c(x1) → d(d(x1))
d(x1) → a(a(x1))

Q is empty.

We use [27] with the following order to prove termination.

Knuth-Bendix order [24] with precedence:
trivial

and weight map:

c_1=207
b_1=72
d_1=99
a_1=49
dummyConstant=1